OpenRaiser/Intern-Atlas huggingface dataset:
Packing Directed Cycles Quarter- and Half-Integrally
Venue: arXiv cs.DM 2020
Year: 2020

The celebrated Erdős-Pósa theorem states that every undirected graph that does not admit a family of $k$ vertex-disjoint cycles contains a feedback vertex set (a set of vertices hitting all cycles in the graph) of size $O(k \log k)$. After being known for long as Younger's conjecture, a similar statement for directed graphs has been proven in 1996 by Reed, Robertson, Seymour, and Thomas. However, in their proof, the dependency of the size of the feedback vertex set on the size of vertex-disjoint cycle packing is not elementary. We show that if we compare the size of a minimum feedback vertex set in a directed graph with the quarter-integral cycle packing number, we obtain a polynomial bound. More precisely, we show that if in a directed graph $G$ there is no family of $k$ cycles such that every vertex of $G$ is in at most four of the cycles, then there exists a feedback vertex set in $G$ of size $O(k^4)$. Furthermore, a variant of our proof shows that if in a directed graph $G$ there is no family of $k$ cycles such that every vertex of $G$ is in at most two of the cycles, then there exists a feedback vertex set in $G$ of size $O(k^6)$. On the way there we prove a more general result about quarter-integral packing of subgraphs of high directed treewidth: for every pair of positive integers $a$ and $b$, if a directed graph $G$ has directed treewidth $Ω(a^6 b^8 \log^2(ab))$, then one can find in $G$ a family of $a$ subgraphs, each of directed treewidth at least $b$, such that every vertex of $G$ is in at most four subgraphs.
Automatic Generation of Efficient Linear Algebra Programs
Venue: arXiv cs.MS 2020
Year: 2020

The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently captured by high-level languages and libraries such as Matlab and Eigen, while the latter expresses the kernels included in the BLAS and LAPACK libraries. Unfortunately, the translation from a high-level computation to an efficient sequence of kernels is a task, far from trivial, that requires extensive knowledge of both linear algebra and high-performance computing. Internally, almost all high-level languages and libraries use efficient kernels; however, the translation algorithms are too simplistic and thus lead to a suboptimal use of said kernels, with significant performance losses. In order to both achieve the productivity that comes with high-level languages, and make use of the efficiency of low level kernels, we are developing Linnea, a code generator for linear algebra problems. As input, Linnea takes a high-level description of a linear algebra problem and produces as output an efficient sequence of calls to high-performance kernels. In 25 application problems, the code generated by Linnea always outperforms Matlab, Julia, Eigen and Armadillo, with speedups up to and exceeding 10x.
Identifiability of Graphs with Small Color Classes by the Weisfeiler-Leman Algorithm
Venue: arXiv cs.CC 2020
Year: 2020

As it is well known, the isomorphism problem for vertex-colored graphs with color multiplicity at most 3 is solvable by the classical 2-dimensional Weisfeiler-Leman algorithm (2-WL). On the other hand, the prominent Cai-Fürer-Immerman construction shows that even the multidimensional version of the algorithm does not suffice for graphs with color multiplicity 4. We give an efficient decision procedure that, given a graph $G$ of color multiplicity 4, recognizes whether or not $G$ is identifiable by 2-WL, that is, whether or not 2-WL distinguishes $G$ from any non-isomorphic graph. In fact, we solve the much more general problem of recognizing whether or not a given coherent configuration of maximum fiber size 4 is separable. This extends our recognition algorithm to graphs of color multiplicity 4 with directed and colored edges. Our decision procedure is based on an explicit description of the class of graphs with color multiplicity 4 that are not identifiable by 2-WL. The Cai-Fürer-Immerman graphs of color multiplicity 4 distinctly appear here as a natural subclass, which demonstrates that the Cai-Fürer-Immerman construction is not ad hoc. Our classification reveals also other types of graphs that are hard for 2-WL. One of them arises from patterns known as $(n_3)$-configurations in incidence geometry.
Self-supervised Learning of Distance Functions for Goal-Conditioned Reinforcement Learning
Venue: arXiv cs.LG 2020
Year: 2020

Goal-conditioned policies are used in order to break down complex reinforcement learning (RL) problems by using subgoals, which can be defined either in state space or in a latent feature space. This can increase the efficiency of learning by using a curriculum, and also enables simultaneous learning and generalization across goals. A crucial requirement of goal-conditioned policies is to be able to determine whether the goal has been achieved. Having a notion of distance to a goal is thus a crucial component of this approach. However, it is not straightforward to come up with an appropriate distance, and in some tasks, the goal space may not even be known a priori. In this work we learn a distance-to-goal estimate which is computed in terms of the number of actions that would need to be carried out in a self-supervised approach. Our method solves complex tasks without prior domain knowledge in the online setting in three different scenarios in the context of goal-conditioned policies a) the goal space is the same as the state space b) the goal space is given but an appropriate distance is unknown and c) the state space is accessible, but only a subset of the state space represents desired goals, and this subset is known a priori. We also propose a goal-generation mechanism as a secondary contribution.
Video Question Generation via Cross-Modal Self-Attention Networks Learning
Venue: arXiv cs.CV 2020
Year: 2020

We introduce a novel task, Video Question Generation (Video QG). A Video QG model automatically generates questions given a video clip and its corresponding dialogues. Video QG requires a range of skills -- sentence comprehension, temporal relation, the interplay between vision and language, and the ability to ask meaningful questions. To address this, we propose a novel semantic rich cross-modal self-attention (SRCMSA) network to aggregate the multi-modal and diverse features. To be more precise, we enhance the video frames semantic by integrating the object-level information, and we jointly consider the cross-modal attention for the video question generation task. Excitingly, our proposed model remarkably improves the baseline from 7.58 to 14.48 in the BLEU-4 score on the TVQA dataset. Most of all, we arguably pave a novel path toward understanding the challenging video input and we provide detailed analysis in terms of diversity, which ushers the avenues for future investigations.
Quantum-inspired canonical correlation analysis for exponentially large dimensional data
Venue: arXiv cs.LG 2020
Year: 2020

Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the conventional CCA algorithm requires polynomial time, we have developed an algorithm that approximates CCA with computational time proportional to the logarithm of the input dimensionality using quantum-inspired computation. The computational efficiency and approximation performance of the proposed quantum-inspired CCA (qiCCA) algorithm are experimentally demonstrated. Furthermore, the fast computation of qiCCA allows us to directly apply CCA even after nonlinearly mapping raw input data into very high dimensional spaces. Experiments performed using a benchmark dataset demonstrated that, by mapping the raw input data into the high dimensional spaces with second-order monomials, the proposed qiCCA extracted more correlations than linear CCA and was comparable to deep CCA and kernel CCA. These results suggest that qiCCA is considerably useful and quantum-inspired computation has the potential to unlock a new field in which exponentially large dimensional data can be analyzed.
Ostraka: Secure Blockchain Scaling by Node Sharding
Venue: arXiv cs.DC 2020
Year: 2020

Cryptocurrencies, implemented with blockchain protocols, promise to become a global payment system if they can overcome performance limitations. Rapidly advancing architectures improve on latency and throughput, but most require all participating servers to process all transactions. Several recent works propose to shard the system, such that each machine would only process a subset of the transactions. However, we identify a denial-of-service attack that is exposed by these solutions - an attacker can generate transactions that would overload a single shard, thus delaying processing in the entire system. Moreover, we show that in common scenarios, these protocols require most node operators to process almost all blockchain transactions. We present Ostraka, a blockchain node architecture that shards (parallelizes) the nodes themselves. We prove that replacing a unified node with an Ostraka node does not affect the security of the underlying consensus mechanism. We evaluate analytically and experimentally block propagation and processing in various settings. Ostraka allows nodes in the network to scale, without costly coordination. In our experiments, Ostraka nodes' transaction processing rate grows linearly with the addition of resources.
Privacy-Preserving Classification with Secret Vector Machines
Venue: arXiv cs.LG 2020
Year: 2020

Today, large amounts of valuable data are distributed among millions of user-held devices, such as personal computers, phones, or Internet-of-things devices. Many companies collect such data with the goal of using it for training machine learning models allowing them to improve their services. User-held data is, however, often sensitive, and collecting it is problematic in terms of privacy. We address this issue by proposing a novel way of training a supervised classifier in a distributed setting akin to the recently proposed federated learning paradigm, but under the stricter privacy requirement that the server that trains the model is assumed to be untrusted and potentially malicious. We thus preserve user privacy by design, rather than by trust. In particular, our framework, called secret vector machine (SecVM), provides an algorithm for training linear support vector machines (SVM) in a setting in which data-holding clients communicate with an untrusted server by exchanging messages designed to not reveal any personally identifiable information. We evaluate our model in two ways. First, in an offline evaluation, we train SecVM to predict user gender from tweets, showing that we can preserve user privacy without sacrificing classification performance. Second, we implement SecVM's distributed framework for the Cliqz web browser and deploy it for predicting user gender in a large-scale online evaluation with thousands of clients, outperforming baselines by a large margin and thus showcasing that SecVM is suitable for production environments.
Learning Structural Graph Layouts and 3D Shapes for Long Span Bridges 3D Reconstruction
Venue: arXiv cs.CV 2020
Year: 2020

A learning-based 3D reconstruction method for long-span bridges is proposed in this paper. 3D reconstruction generates a 3D computer model of a real object or scene from images, it involves many stages and open problems. Existing point-based methods focus on generating 3D point clouds and their reconstructed polygonal mesh or fitting-based geometrical models in urban scenes civil structures reconstruction within Manhattan world constrains and have made great achievements. Difficulties arise when an attempt is made to transfer these systems to structures with complex topology and part relations like steel trusses and long-span bridges, this could be attributed to point clouds are often unevenly distributed with noise and suffer from occlusions and incompletion, recovering a satisfactory 3D model from these highly unstructured point clouds in a bottom-up pattern while preserving the geometrical and topological properties makes enormous challenge to existing algorithms. Considering the prior human knowledge that these structures are in conformity to regular spatial layouts in terms of components, a learning-based topology-aware 3D reconstruction method which can obtain high-level structural graph layouts and low-level 3D shapes from images is proposed in this paper. We demonstrate the feasibility of this method by testing on two real long-span steel truss cable-stayed bridges.
A Mathematical Analysis of an Election System Proposed by Gottlob Frege
Venue: arXiv cs.GT 2020
Year: 2020

In 1998 a long-lost proposal for an election law by Gottlob Frege (1848--1925) was rediscovered in the Thüringer Universitäts- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run. We find that through a slight modification of Frege's original method even stronger proportionality guarantees can be achieved. This modified version of Frege's method also provides a novel solution to the apportionment problem, which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties.
Improving short text classification through global augmentation methods
Venue: arXiv cs.CL 2020
Year: 2020

We study the effect of different approaches to text augmentation. To do this we use 3 datasets that include social media and formal text in the form of news articles. Our goal is to provide insights for practitioners and researchers on making choices for augmentation for classification use cases. We observe that Word2vec-based augmentation is a viable option when one does not have access to a formal synonym model (like WordNet-based augmentation). The use of \emph{mixup} further improves performance of all text based augmentations and reduces the effects of overfitting on a tested deep learning model. Round-trip translation with a translation service proves to be harder to use due to cost and as such is less accessible for both normal and low resource use-cases.
A duality theoretic view on limits of finite structures
Venue: arXiv cs.LO 2020
Year: 2020

A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of measures arises --- via Stone-Priestley duality and the notion of types from model theory --- by enriching the expressive power of first-order logic with certain ``probabilistic operators''. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality-theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively.
Characterization of Overlap in Observational Studies
Venue: arXiv cs.LG 2020
Year: 2020

Overlap between treatment groups is required for non-parametric estimation of causal effects. If a subgroup of subjects always receives the same intervention, we cannot estimate the effect of intervention changes on that subgroup without further assumptions. When overlap does not hold globally, characterizing local regions of overlap can inform the relevance of causal conclusions for new subjects, and can help guide additional data collection. To have impact, these descriptions must be interpretable for downstream users who are not machine learning experts, such as policy makers. We formalize overlap estimation as a problem of finding minimum volume sets subject to coverage constraints and reduce this problem to binary classification with Boolean rule classifiers. We then generalize this method to estimate overlap in off-policy policy evaluation. In several real-world applications, we demonstrate that these rules have comparable accuracy to black-box estimators and provide intuitive and informative explanations that can inform policy making.
A Geometric Approach to Rank Metric Codes and a Classification of Constant Weight Codes
Venue: arXiv cs.IT 2020
Year: 2020

In this work we develop a geometric approach to the study of rank metric codes. Using this method, we introduce a simpler definition for generalized rank weight of linear codes. We give a complete classification of constant rank weight code and we give their generalized rank weights.
DeepXDE: A deep learning library for solving differential equations
Venue: arXiv cs.LG 2020
Year: 2020

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs), which embed a PDE into the loss of the neural network using automatic differentiation. The PINN algorithm is simple, and it can be applied to different types of PDEs, including integro-differential equations, fractional PDEs, and stochastic PDEs. Moreover, from the implementation point of view, PINNs solve inverse problems as easily as forward problems. We propose a new residual-based adaptive refinement (RAR) method to improve the training efficiency of PINNs. For pedagogical reasons, we compare the PINN algorithm to a standard finite element method. We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an education tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering. Specifically, DeepXDE can solve forward problems given initial and boundary conditions, as well as inverse problems given some extra measurements. DeepXDE supports complex-geometry domains based on the technique of constructive solid geometry, and enables the user code to be compact, resembling closely the mathematical formulation. We introduce the usage of DeepXDE and its customizability, and we also demonstrate the capability of PINNs and the user-friendliness of DeepXDE for five different examples. More broadly, DeepXDE contributes to the more rapid development of the emerging Scientific Machine Learning field.
Decoding and Repair Schemes for Shift-XOR Regenerating Codes
Venue: arXiv cs.IT 2020
Year: 2020

Decoding and repair schemes are proposed for shift-exclusive-or (shift-XOR) product-matrix (PM) regenerating codes, which outperform the existing schemes in terms of both communication and computation costs. In particular, for the shift-XOR minimum bandwidth regenerating (MBR) codes, our decoding and repair schemes have the optimal transmission bandwidth and can be implemented in-place without extra storage space for intermediate XOR results. Technically, our schemes involve an in-place algorithm for solving a system of shift-XOR equations, called \emph{shift-XOR elimination}, which does not have the bandwidth overhead generated by shift operations as in the previous zigzag algorithm and has lower computation complexities compared with the zigzag algorithm. The decoding and repair of shift-XOR MBR/MSR codes are decomposed into a sequence of systems of shift-XOR equations, and hence can be solved by a sequence of calls to the shift-XOR elimination. As the decompositions of the decoding and repair depend only on the PM construction, but not the specific shift and XOR operations, our decoding and repair schemes can be extended to other MBR/MSR codes using the PM construction. Due to its fundamental role, the shift-XOR elimination is of independent interest.
Malware in the SGX supply chain: Be careful when signing enclaves!
Venue: arXiv cs.CR 2020
Year: 2020

Malware attacks are a significant part of the new software security threats detected each year. Intel Software Guard Extensions (SGX) are a set of hardware instructions introduced by Intel in their recent lines of processors that are intended to provide a secure execution environment for user-developed applications. To our knowledge, there was no serious attempt yet to overcome the SGX protection by exploiting the weaknesses in the software supply chain infrastructure, namely at the level of the development, build or signing servers. While SGX protection does not specifically take into consideration such threats, we show in the current paper that a simple malware attack exploiting a separation between the build and signing processes can have a serious damaging impact, practically nullifying SGX integrity protection measures. We also explore two possible mitigations against the attack, one centralized leveraging SGX itself, and one distributed that relies on a smart contract deployed on a blockchain infrastructure. Our evaluation shows that both methods are feasible in practice and their added costs are acceptable for the offered protection.
Deep Reinforcement-Learning-based Driving Policy for Autonomous Road Vehicles
Venue: arXiv cs.RO 2020
Year: 2020

In this work the problem of path planning for an autonomous vehicle that moves on a freeway is considered. The most common approaches that are used to address this problem are based on optimal control methods, which make assumptions about the model of the environment and the system dynamics. On the contrary, this work proposes the development of a driving policy based on reinforcement learning. In this way, the proposed driving policy makes minimal or no assumptions about the environment, since a priori knowledge about the system dynamics is not required. Driving scenarios where the road is occupied both by autonomous and manual driving vehicles are considered. To the best of our knowledge, this is one of the first approaches that propose a reinforcement learning driving policy for mixed driving environments. The derived reinforcement learning policy, firstly, is compared against an optimal policy derived via dynamic programming, and, secondly, its efficiency is evaluated under realistic scenarios generated by the established SUMO microscopic traffic flow simulator. Finally, some initial results regarding the effect of autonomous vehicles' behavior on the overall traffic flow are presented.